Continuity mistake: When Arthur is listing the genres of the film, his legs go from on the floor to one raised and back between shots. (00:02:10)
Continuity mistake: When Doug and Arthur are sat at the dinner table, Arthur's hands go from on the table to clasped between shots. (00:07:45)
Queasy Rider - S2-E1
Visible crew/equipment: When Doug and Carrie are arguing over the bike a white tape marker can be seen on the floor. (00:09:20)
Queasy Rider - S2-E1
Continuity mistake: When Spence is talking to Carrie at the restaurant at the start, Spence has his hands out in front of him. Camera cuts to another angle and now he has his drink in his hand. (00:01:45)
Maybe Baby - S1-E25
Continuity mistake: When Doug sits down with Arthur in the night, the magazine on the table changes between shots. (00:11:50)
Maybe Baby - S1-E25
Continuity mistake: When Doug tells Deacon that he and Carrie are trying for a baby, Deacon has both hands on his knees, camera changes and he's got 1 hand and 1 elbow on his knees. (00:09:50)
Hungry Man - S1-E21
Visible crew/equipment: When Spence is pacing there are tape markers visible on the floor where he turns. (00:17:20)
Train Wreck - S1-E20
Continuity mistake: When Arthur is rewriting his epitaph, the pad and pencil keep moving between shots. (00:12:10)
Train Wreck - S1-E20
Continuity mistake: When Julie goes to get her jacket, Doug's board swaps hands instantly. (00:03:40)
Fixer Upper - S1-E12
Continuity mistake: At the start, the items in Carrie's hands swap hands instantly. (00:00:10)
Continuity mistake: At the end, the shawl around Carrie's shoulder is either covering her shoulder or not depending on the shot. (00:20:50)
Visible crew/equipment: When Richie is explaining about getting rid of the car, tape markers are visible by Doug's feet. (00:14:40)
Visible crew/equipment: After the first drive in the Mini, a stage light is reflected clear as day in the bonnet. (00:13:20)
Continuity mistake: When the guy chucks his cheque book into the basket, it reappears in his hand a second later. (00:11:20)
Revealing mistake: As Carrie skids into the parking spot at the start, skid marks are visible on the floor from previous takes. (00:00:30)
Road Rayge - S1-E9
Continuity mistake: When trying to get Doug to drive after the Jets' game, Ray's press pass goes from white to green instantly. (00:09:20)
Continuity mistake: In the first classroom scene there are two people sat to Doug's right. These people then vanish a few seconds later. (00:07:55)
Answer: To answer the question directly. Carrie and Doug do not have a biological child during the show's main run. In season 3 or 4 finale (cant remember which) Carrie has a miscarriage. Later on in the show they find out Carrie has 1 working ovary. Thus reducing the chance of them conceiving. By the final season, they couple agree to adopt from China and go to collect their child in the show's final episode. While on the flight back from China it's revealed that Carrie is once again pregnant. However the last scene of the show is a flash forward showing that Carrie goes full term with that child and they are struggling with both kids.
Ssiscool ★
Adding on to this answer, I read somewhere that producers were afraid of the show having a "before baby" feeling and then an "after baby" feeling. Some fans feel that main characters, or the show in general, decline in quality after a major change. For example, Jesse and Rebecca on "Full House" after they had twin sons, and Daphne on "Frasier" after she married Niles.